PH-POS-001

Name: Positivity violation

Severity: error

Input modes: adapter+dump

PH-POS-001 is a pointwise positivity check: under a boundary condition that preserves sign (homogeneous Dirichlet with non-negative data; the heat eigenfunction decay regime), the surrogate’s field \(u\) must satisfy \(u \ge \mathrm{floor}\) everywhere (default floor = 0). The raw value is the minimum field value; the violation fraction is the share of cells below the floor.

The rule fires (FAIL) when any cell is below the floor. The reported reason names the cell count and the fraction so the user can distinguish a single boundary-artefact violation from a systemic sign-flipping bias. The rule emits SKIPPED when the configured boundary condition does not preserve sign — for example, inhomogeneous Neumann or a source term that admits sign change.

PH-POS-001’s external-validation anchor stack rests on Evans §2.2.3 Theorem 4 (Poisson positivity under homogeneous Dirichlet with \(f \ge 0\)) and §2.3.3 Theorem 4 (heat eigenfunction sign preservation). See CITATION.md for the full provenance and AUDIT.md for the pre-execution enumerate-the-splits verification.